Mobile communications devices have become an integral part of society over the last two decades. Indeed, more than eighty-two percent of Americans own a mobile communications device, for example, a cell phone. The typical mobile communications device includes an antenna, and a transceiver coupled to the antenna. The transceiver and the antenna cooperate to transmit and receive communications signals.
Before transmission, the typical mobile communications device modulates digital data onto an analog signal. As will be readily appreciated by the skilled person, there is a plurality of modulations available for most applications. Some particularly advantageous modulations include, for example, continuous phase modulation (CPM). The constant envelope characteristics of this modulation provide for lower energy demands on the power amplifier of mobile communications devices, for example, by reducing the peak-to-average power ratio (PAPR), increasing average transmit power (providing greater transmission range), and increasing amplifier efficiency, i.e. allowing the use of non-linear amplifiers such as Class C amplifiers. Moreover, CPM provides for efficient use of available bandwidth.
A potential drawback of CPM modulations, for example, Gaussian Minimum-shift keying (GMSK), is the use of the inherent memory of the modulation when demodulating/decoding the waveform in order to obtain good demodulator performance. When the mobile communications device receives a transmitted signal which uses a modulation with memory, the decoder uses not only the current signal portion to demodulate but in addition uses information from previous signal portions, i.e. memory, to demodulate the current signal. In other words, the phase of the transmitted signal is dependent on previous signaling intervals. Decoding modulations with memory increases the computational and memory demands on the transceiver, i.e. a maximum likelihood sequence estimator (MLSE) is typically used to demodulate modulations with memory, thereby increasing the complexity of the device, which may be undesirable in a limited power compact mobile device. More so, when the received signal has a multipath component to it, the size of the MLSE trellis structure used to demodulate the signal grows exponentially, which may make practical implementation in a mobile communications device difficult.
Digital communications theory has undergone a significant transformation in the last two decades due mainly to the discovery of iterative codes. Serially concatenated iterative codes are composed of two forward error correction (FEC) codes that are separated by a random interleaver. The outer code can be recursive or non-recursive in nature, but the inner code must be recursive in order for there to be interleaver gains when soft information is exchanged between the two codes. An approach investigated by several researchers was the possibility of using CPM waveforms as rate 1 recursive inner codes and combining them with simple convolutional FEC outer codes. Researchers showed that this approach could achieve close to Shannon performance.
When serially concatenated codes, which use CPM waveforms as the inner code, are used on multipath fading channels, the complexity of the inner MLSE soft-input soft-output (SISO) algorithms can be quite high, especially when the decoder must iterate several times between the inner CPM/Multipath SISO and the outer FEC SISO. This is due to the fact that CPM waveforms may require a MLSE for proper demodulation of the waveform, and the additional requirement of handling multipath further may increase the size of the MLSE in an exponential manner.
Most SISO algorithms, for example, the BCJR algorithm, may require forward and backward recursions on the trellis the algorithms operate on, i.e. inner CPM/Multipath trellis or outer FEC trellis, before computing the extrinsic information which will be provided to the other SISO device, for example, inner SISO device generates extrinsic information for outer SISO device. Both forward and backward recursions require the computation of independent path metrics for each direction. In an effort to reduce the trellis structure of SISO decoders, some approaches include reducing the number of states in the trellis, i.e. reduced state trellis. For example, U.S. Pat. No. 7,096,412 to Chen et al. discloses a reduced complexity iterative decoding method. Nevertheless, the forward/backward SISO computation of the reduced states and survivor paths can still represent a serious computational workload for the receiver device, especially in mobile applications.